Question

In this problem you will be looking at information relating to small business success and failures in the state of Indiana.  While working at First Source Bank you will be asked to write a report for the SBA relating your findings.

A study of the survival of small businesses chose a SRS from the Yellow Pages listings of food-and-drink businesses in 12 counties in central Indiana.  For various reasons, the study got no response from 45% of the businesses chosen.  Interviews were completed with 148 businesses.  Three years later, 22 of these businesses failed.  Find a 95% confidence interval for the percent of all small businesses in this class that fail within three years.  Based on this study, how large of a sample would be needed to reduce the margin of error to 4 points?

The authors of the study hoped that their findings describe the population of all small businesses, what makes this unlikely and what population do you think the study findings describe?

More additional information.  Of the 148 small businesses, 106 were headed by men and 42 by women.  Of the failed businesses, 15 were men’s and 7 were women’s.  Is there a significant difference between the percent of failure by gender?

look at the  sample proportions of men and women failures.  If we increased the sample size to 30 times the original so that the failures of men and women were 450 out of 3180 (men) and 210 out of 1260 (women),  find a new confidence interval at 95% and discus the effect of larger samples on the confidence interval.

Answer 1

45% of business didn't answer.

55% of business gave interview. / 148 businesses chose to answer the survey.

Since no info is available for the non-responding business, we will choose to ignore them in our data.

22 out of 148 businesses failed within 3 years.

Therefore proportion of business failing = p =22/148 =0.148 .

A 95% CI looks like :

Your last question is not clear.